Analysis of a Flexible Cylindrical Structure for a Harmonic Motor Drive

This paper presents an analysis of the actuation requirements of the flexible spline of a harmonic motor. The analysis accounts for the initial strain distribution required to bring the flexible spline into contact with the rigid spline, and proceeds to the derivation of the additional stress required to produce a given contact force for torque generation. An expression for the two-dimensional stress distribution in an annular ring subject to an external radial force is found analytically and verified by a finite-element simulation. The results show that the stress values are proportional to the spline radius and the applied force, and inversely proportional to the spline length and the square of the thickness. A stiffness analysis of a more realistic three-dimensional flexible structure is then used to show that the two-dimensional analysis gives conservative design results and can be used for the choice of appropriate actuator characteristics.